Applications of the Second Kind Chebyshev Polynomials of Bi-

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Abstract

The purpose of this paper is to use the second kind Chebyshev polynomials to introduce a new class of analytic and bi-univalent functions associating bi-starlike and biconvex λ-pseudo functions with Sakaguchi type functions deﬁned in the open unit disk. We determinate upper bounds for the initial Taylor-Maclaurin coeﬃcients |a2| and |a3| for functions in this class. 1

Results & Lemmas (4)

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Theorem 2.1. Theorem 2.1. For 0 ≤δ ≤1, λ ≥1, m, n ∈C with m ̸= n; |n| ≤1 and t ∈ 1 2, 1 , let f be in the class RΣ(δ, λ, m, n; t). Then |a2| ≤ 2t √…

Theorem 2.1. For 0 ≤δ ≤1, λ ≥1, m, n ∈C with m ̸= n; |n| ≤1 and t ∈ 1 2, 1 , let f be in the class RΣ(δ, λ, m, n; t). Then |a2| ≤ 2t √ 2t v u u t

Corollary 2.1. Corollary 2.1. For λ ≥1 and t ∈ 1 2, 1 , let f be in the class RS Σ(λ; t). Then |a2| ≤ t √ 2t p |(λ −2λ2 −1) t2 + λ2| and |a3| ≤t2 λ2 +

Corollary 2.1. For λ ≥1 and t ∈ 1 2, 1 , let f be in the class RS Σ(λ; t). Then |a2| ≤ t √ 2t p |(λ −2λ2 −1) t2 + λ2| and |a3| ≤t2 λ2 +

Corollary 2.2. Corollary 2.2. [20] For t ∈ 1 2, 1 , let f be in the class Fsc Σ (t). Then |a2| ≤ t √ t p |2 −5t2| and |a3| ≤t(3t + 4)

Corollary 2.2. [20] For t ∈ 1 2, 1 , let f be in the class Fsc Σ (t). Then |a2| ≤ t √ t p |2 −5t2| and |a3| ≤t(3t + 4)

Corollary 2.3. Corollary 2.3. [19] For t ∈ 1 2, 1 , let f be in the class DS Σ(1, t). Then |a2| ≤ t √ 2t p |2t2 −1| and |a3| ≤t(t + 1).

Corollary 2.3. [19] For t ∈ 1 2, 1 , let f be in the class DS Σ(1, t). Then |a2| ≤ t √ 2t p |2t2 −1| and |a3| ≤t(t + 1).

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Results & Lemmas (4)

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